The \(K^+\rightarrow \pi ^+\nu \bar{\nu }\)  decay is among the most promising modes to search for non-SM
signals in flavour physics, and it probes higher mass scales than
other rare meson decays. The largest deviations from SM predictions
are expected in models with new sources of flavour violation, where
constraints from \(B\)  physics are weaker [1]}, [2]}. Models with tree-level FCNCs of left- or right-handed
chirality produce specific correlation patterns between the branching
ratios of \(K_L\rightarrow \pi ^0\nu \bar{\nu }\)  and \(K^+\rightarrow \pi ^+\nu \bar{\nu }\)  decay modes, which are constrained by the
value of the CP-violation parameter \(\epsilon _K\) 
[3]}, [4]}. Present experimental constraints limit the
range of variation within supersymmetric models
[5]}, [6]}, [7]}. The \(K^+\rightarrow \pi ^+\nu \bar{\nu }\)  decay is also sensitive to
some aspects of lepton flavour non-universality [8]} and can
constrain leptoquark models [9]}, [10]}.
